Comedian, actress and marriage equality advocate Magda Szubanski has taken aim at prime minister Malcolm Turnbull for his “gloating” speech on same-sex marriage, saying the prime minister should check his demeanour.

Szubanski, who is best known for creating and starring as the character of Sharon in Kath & Kim, was one of the most prominent faces of the “yes” campaign in the national survey on same-sex marriage.

She told reporters on Tuesday that she thought the prime minister's speech, which was glowing in its assessment of the survey, was tone deaf, given the deeply negative experience many LGBTI people had during the same-sex marriage vote.

In his speech, delivered around lunchtime on Monday, Turnbull noted that he was “the first prime minister of Australia to be unequivocally and consistently in support of legalising same-sex marriage”.

“It will be forever to the credit of the Coalition that this momentous social change occurred with the overwhelming mandate of the Australian people, under a Coalition government,” he said.

Turnbull also lauded the postal survey on same-sex marriage, which was opposed by much of the LGBTI community, as “one of the most remarkable political events of my lifetime”.

He said the 80% turnout “proved what we always said: that Australians wanted to have their say”, and that it was a day every Australian should be proud of.

“Proud that we can conduct and did conduct, despite all the naysayers, a very civil debate,” he said. “Proud that given the opportunity to vote, far from being apathetic as the naysayers predicted, we participated in such enormous numbers.

“This is a day to be especially proud that all of our friends, our colleagues, our neighbours, our brothers, our sisters, can marry the people they love.”

Asked what she thought of the speech at a press conference on Tuesday, Szubanski said “Look” before taking a long pause.

“Having had so much feedback from people in terrible pain, to see the prime minister gloating and taking credit was a little bit hard to swallow when really every obstacle has been put in the way of this happening, and he has caved in to all of it,” she said.

“So I think he should check in a little bit with his demeanour with that stuff.”

Szubanski said the survey “may have saved [Turnbull’s] political skin”, but given the impact of the survey, “it is not a moment to stand in the parliament and gloat”.

A national survey of more than 3,000 LGBTI Australians conducted last month found four-in-five respondents had been adversely affected by the same-sex marriage vote, and two thirds had found it worse than they thought it would be.

Szubanski said Turnbull should “now be a leader” and criticised him for lending support to some of the amendments to the bill moved by a bloc of conservative opponents to same-sex marriage.

“The fact there is a small minority the prime minister and other people are caving in to — I think there's going to be a lot of cross voters about this, because it's reflective of so many issues.”

Turnbull has indicated he will vote in favour of amendments that would allow civil celebrants to refuse to marry gay couples, and that would ensure charities can retain their status despite holding a view against same-sex marriage.

Several amendments are expected to be moved in the House of Representatives later this week after a lengthy list of speakers wraps up, likely on Wednesday evening.